Accurate Evaluation of Polynomials in Legendre Basis

Algorithm 2

Split of a floating point number into two parts.

function [𝑥,𝑦]=𝑆𝑝𝑙𝑖𝑡(𝑎)

𝑐=𝑓𝑎𝑐𝑡𝑜𝑟⊗𝑎 (in double precision factor =2²⁷+1)

𝑥=𝑐⊖(𝑐⊖𝑎)

𝑦=𝑎⊖𝑥